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Intern  S
Joined: 26 Apr 2018
Posts: 38
Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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22 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:38) correct 34% (02:41) wrong based on 172 sessions

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Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3674
Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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Beqa chose an excellent method. +1

We can also find amounts of each juice in a 4:1 mix, and set them in a ratio

To find concentration of, say, OJ in A, sum the ratio parts.
Concentration = $$\frac{part}{total}=\frac{L}{L+OJ}$$

A mix: $$\frac{L}{OJ}=\frac{1}{3}$$
Total parts: (1 + 3) = 4
A, concentration of $$L = \frac{1}{4}$$
A, concentration of $$OJ=\frac{3}{4}$$

B mix: $$\frac{L}{OJ}=\frac{5}{3}$$
Total parts: (5 + 3) = 8
B, concentration of $$L = \frac{5}{8}$$
B, concentration of $$OJ=\frac{3}{8}$$

Drink A is mixed with drink B in the ratio of 4:1 to form drink C
So the amount of A in the resultant drink C is 4 times as much as B

Lemon juice only in 4A + 1B?

$$(4)(\frac{1}{4})+(1)(\frac{5}{8})=$$

$$(1+\frac{5}{8})=(\frac{8}{8}+\frac{5}{8})=\frac{13}{8}$$

Orange juice only in 4A+1B?
$$(4)(\frac{3}{4})+(1)(\frac{3}{8})=$$

$$(3+\frac{3}{8})=(\frac{24}{8}+\frac{3}{8})=\frac{27}{8}$$

Ratio of lemon juice to orange juice in C?
C = mix of 4A and 1B, as above

$$\frac{L}{OJ}=\frac{(\frac{13}{8})}{(\frac{27}{8})}=(\frac{13}{8}*\frac{8}{27})=\frac{13}{27}$$

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Intern  B
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GMAT 1: 720 Q50 V36 GMAT 2: 740 Q50 V40 GPA: 3.67
Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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7
Very interesting question. I would like to use: SMART NUMBER strategy, in which we use real numbers to avoid complex calculations.

Let's look at solution C, which is made from 4 parts of solution A and 1 part of solution B. Hence, you may want start with solution B.

Let's take 8ml of B, in which there are 5ml Lemon and 3ml Orange.
We need 8x4=32ml of A, in which there are 8ml Lemon and 24ml Orange.
Put A and B together, we have 13ml Lemon and 27ml Orange ==> D. 13/27
##### General Discussion
Intern  S
Joined: 05 Jan 2017
Posts: 34
Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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In A -
l -> 1/4 ------(A1)
O -> 3/4

In B -
l -> 5/8 ------ (A2)
o -> 3/8

let x be the Avg.

use weighted average formula -
w1/w2=(A2–Aavg)/(Aavg–A1)

(5/8 - x)/(x-1/4) = 4/1 --------- (this ratio is given in the question)
on solving =>
x=13/40
so lemon is 13
similarly solve for orange or we can just do 40-13=27
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VP  P
Joined: 07 Dec 2014
Posts: 1221
Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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let x=ratio of lemon juice to total drink C
4*1/4+1*5/8=5x
x=13/40
13/(40-13)=13/27=13:27 ratio of lemon juice to orange juice in drink C
D
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Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

We have the following two ratios:

For A:

L : O = x : 3x

For B:

L : O = 5y : 3y

In drink C, we know the ratio of A : B is 4: 1; thus, we can set up the proportion:

(x + 3x)/(5y + 3y) = 4/1

4x/8y = 4

4x = 32y

x = 8y

If we let y = 1, then x = 8. So in drink A, we have L = 8 and O = 24, and in drink B, we have L = 5 and O = 3. So the total amount of L in drink C is 8 + 5 = 13 and the total amount of O in drink C is 24 + 3 = 27. So the ratio of L to O is 13/27.

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Manager  G
Joined: 07 Aug 2018
Posts: 107
Location: United States (MA)
GMAT 1: 560 Q39 V28 GMAT 2: 670 Q48 V34 Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

source gmat tutor

Little different approach:

$$Drink$$ $$A$$: $$\frac{1}{4}$$ $$L$$ $$(lemon)$$; $$Drink$$ $$B$$: $$\frac{5}{8}$$ $$L$$ $$(lemon)$$

$$Drink$$ $$C$$: $$\frac{4}{5}Drink$$ $$A$$ and $$\frac{1}{5}Drink$$ $$B$$

Therefore percentage of $$L$$ in $$Drink$$ $$C$$ is:

$$\frac{4}{5}*\frac{1}{4} + \frac{1}{5}*\frac{5}{8} = \frac{13}{40}$$

Hence ratio of $$Lemon$$ to $$Orange$$ in $$Drink$$ $$C$$ is $$13:27$$
_________________ Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l   [#permalink] 05 Oct 2018, 06:57
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